Answer:
Option 2nd is correct
10.5 feet is the longest the room can be
Step-by-step explanation:
Area of Rectangle(A) is given by:
....[1]
where, l is the length and w is the width of the rectangle.
As per the statement:
A rectangular room must have a maximum area of 84 square feet.
⇒A = 84 square feet.
It is also given that If the room is to be 8 feet wide.
⇒ w = 8 feet
Substitute the given values in [1] we have;

Divide both sides by 8 we have;

or
l = 10.5 feet
Therefore, the longest the room can be 10.5 feet